Exam 11: Statistical Inference Concerning Variance

Which of the following is the formula for the sample variance s² when used as an estimate of σ² for a random sample of n observations from a population?

Which of the following is a feature of the F distribution?

A supermarket has just added a new cash register to reduce the waiting times of the customers during weekends.Because a new cash register has been added,the customers expect their waiting time to be less than the waiting time had been before the cash register was added.Suppose the sample variance of the waiting times for 25 customers before adding the new cash register is minutes,while the sample variance of the waiting times for 25 customers after adding the cash register is minutes.The manager of the supermarket believes that the waiting times are normally distributed and that the two samples are drawn independently. a.Develop the hypotheses to test whether the ratio of two population variances is less than 1. b.Calculate the appropriate test statistic. c.Using the p-value approach,determine the decision rule at the 5% significance level. d.What is the conclusion? Given that all other criteria are satisfied,should the supermarket continue with the new cash register?

The F distribution depends on _____ degrees of freedom.

The estimator of used in the inference regarding the ratio of two population variances is .

Annual growth rates for individual firms in the toy industry tend to fluctuate dramatically,depending on consumers' tastes and current fads.Consider the following growth rates (in percent)for two companies in this industry,Hasbro and Mattel. Which of the following are the null and alternative hypotheses in order to determine if the variance of growth rates differs for the two firms?

The manager of a video library would like the variance of the waiting times of the customers not to exceed 2.30 minutes-squared.He would like to add an additional billing counter if the variance exceeds the cut-off.He checks the recent sample data.For a random sample of 24 customer waiting times,he arrives at a sample variance of 3.8 minutes-squared.The manager assumes the waiting times to be normally distributed.Which of the following is the correct approximation of the p-value used to conduct this test?

Using the critical value approach,conduct the following hypothesis test at the 1% significance level:

The specification of the confidence interval for the ratio of two population variances is based on the assumption that the sample variances are computed from ____________ drawn samples from two normally distributed populations.

All distributions are __________ skewed.

Statistical inferences pertaining to σ² are based on which of the following distributions?

Placing the larger sample variance in the numerator of the statistic allows one to focus only on the _____ tail of the distribution.

A financial analyst maintains that the risk,measured by the variance,of investing in emerging markets is more than 280(%)².Data on 20 stocks from emerging markets revealed the following sample results: = 12.1% and s² = 361(%)² .Assume that the returns are normally distributed.Which of the following is the correct value of the test statistic?

(Use Excel)The following are the prices (in $1,000s)of 20 houses sold recently in Vancouver,Washington.A real estate agent believes that the standard deviation of house prices is less than 70 units,where each unit equals $1,000.Assume house prices are normally distributed. a.State the null and the alternative hypotheses for the test. b.Calculate the value of the test statistic. c.Use Excel's function (either CHISQ.DIST.RT or CHISQ.DIST)to calculate the p-value. d.At α = 0.10,what is the conclusion? Is the agent's claim supported by the data?

Amie Jackson,a manager at Sigma travel services,makes every effort to ensure that customers attempting to make online reservations do not have to wait too long to complete the reservation process.The travel website is open for reservations 24 hours a day,and Amie regularly checks the website for the waiting time to maintain consistency in service.She uses the following independently drawn samples of wait time during two peak hours,morning 8a.m.to 10 a.m.and evening 7p.m.to 9p.m. ,for the analysis.Assume that wait times are normally distributed. At the 10% significance level,which of the following is the correct conclusion?

A random sample of 21 pages is used to estimate the population variance of the number of typographical errors in a book.The sample mean and sample standard deviation are calculated as 7.34 and 5.11,respectively.Assume that the population is normally distributed. a.Construct a 95% interval estimate of the population variance. b.Construct a 99% interval estimate of the population variance. c.Use your answers to discuss the impact of the confidence level on the width of the interval.

The administrator of a college is concerned about the students using cell phones for texting during the class hours.She randomly selects 25 students to check if the variance of the number of students in the college using cell phones during the class hours is less than 12.She arrives at a sample variance of 7.She assumes the distribution to be normal. a.State the appropriate null and alternative hypotheses for the test. b.Compute the value of the test statistic. c.Use the critical value approach to test the administrator's concern at α = 0.10. d.Repeat the test at α = 0.01.

Find the value x for which a.P( ≥ x)= 0.005. b.P( < x)= 0.025. c.P( ≥ x)= 0.005. d.P( < x)= 0.025.

A financial analyst examines the performance of two mutual funds and claims that the variances of the annual returns for the bond funds differ.To support his claim,he collects data on the annual returns (in percent)for the years 2001 through 2010.The analyst assumes that the annual returns for the two emerging market bond funds are normally distributed.Use the following summary statistics. The competing hypotheses are Which of the following is the critical F value at the 10% significance level?

The values taken from a normally distributed population are 21 23 25 27 28 35 30 32 33. Which of the following is a 95% confidence interval for the population variance.